Prepare the vegetables

• Grate the carrots (or use pre-shredded carrots).
• Cut the broccoli into bite-size pieces.
• Grate the cheddar cheese yourself and set aside.

Sweat the onion and garlic

• Melt the unsalted butter in a large pot.
• Add the diced onion and cook, stirring, for 4 minutes.
• Add the minced garlic and cook for 20 seconds.

Make the roux

• Add the all-purpose flour and cook, stirring constantly, for 1 minute.

Add the liquid and vegetables

• Pour in the whole milk and chicken stock, whisking to avoid lumps.
• Add the broccoli and grated carrots.
• Simmer for about 10 minutes, stirring occasionally so it doesn't stick to the bottom.

Finish with cream and cheese

• Turn off the heat before adding the cream and cheese.
• Stir in the heavy cream and the grated cheddar cheese until melted and smooth.
• Season with salt to taste and serve.